Overpartition $M2$-rank differences, class number relations, and vector-valued mock Eisenstein series

Brandon Williams

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arXiv · 1708.02569

Overpartition $M2$-rank differences, class number relations, and vector-valued mock Eisenstein series

Brandon Williams

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Abstract

We prove that the generating function of overpartition $M2$-rank differences is, up to coefficient signs, a component of the vector-valued mock Eisenstein series attached to a certain quadratic form. We use this to compute analogs of the class number relations for $M2$-rank differences. As applications we split the Kronecker-Hurwitz relation into its "even" and "odd" parts and calculate sums over Hurwitz class numbers of the form $\sum_{r \in \mathbb{Z}} H(n - 2r^2)$.

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Brandon Williams. 2017-08-08. Overpartition $M2$-rank differences, class number relations, and vector-valued mock Eisenstein series. https://arxiv.org/abs/1708.02569

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